B. Mamporia

On the Ito Formula in a Banach Space

abstract:
If $(W_t)_{t\in[\,0,1]}$ is a Wiener process in an arbitrary separable Banach space $X$, $\psi:[\,0,1]\times X\to Y$ is a continuous function with values in another separable Banach space, and $\psi$ has continuous Frechet derivatives $\psi'_t$, $\psi'_x$ and $\psi_{xx}''$, then the Ito formula is obtained for $\psi(t,W_t)$. \par The method is based on the concept of covariance operator and a special construction of the Ito stochastic integral.